Frequency-Domain Circuit Model and Analysis of Coupled Magnetic Resonance Systems

An explicit frequency-domain circuit model for the conventional coupled magnetic resonance system (CMRS) is newly proposed in this paper. Detail circuit parameters such as the leakage inductances, magnetizing inductances, turn-ratios, internal coil resistances, and source/load resistances are explicitly included in the model. Accurate overall system efficiency, DC gain, and key design parameters are deduced from the model in closed form equations, which were not available in previous works. It has been found that the CMRS can be simply described by an equivalent voltage source, resistances, and ideal transformers when it is resonated to a specified frequency in the steady state. It has been identified that the voltage gain of the CMRS was saturated to a specific value although the source side or the load side coils were strongly coupled. The phase differences between adjacent coils were ${\pi}/2$, which should be considered for the EMF cancellations. The analysis results were verified by simulations and experiments. A detailed circuit-parameter-based model was verified by experiments for 500 kHz by using a new experimental kit with a class-E inverter. The experiments showed a transfer of 1.38 W and a 40 % coil to coil efficiency.